In recent years, various resonators using piezoelectric materials such as a film bulk acoustic resonator (FBAR) and a surface acoustic wave (SAW) resonator have come into practical use as small and high-performance resonators. Especially, the film bulk acoustic resonator has been recently attracting attention in view of uses where a high resonant frequency such as 5 GHz or more is required, because the resonant frequency thereof is easily increased due to its structure compared to the surface acoustic wave resonator.
As described in U.S. Pat. No. 5,872,493, the film bulk acoustic resonator is basically constituted of an upper electrode, a lower electrode and a piezoelectric film interposed therebetween. A certain resonance characteristics can be obtained by applying a high frequency signal between the upper electrode and the lower electrode. The resonant frequency of the film bulk acoustic resonator mainly depends on film thicknesses of the upper electrode, the lower electrode and the piezoelectric film. These film thicknesses are set by referring to a wavelength determined by a ratio of an acoustic velocity of a bulk wave to the resonant frequency (acoustic velocity/resonant frequency). Here, the acoustic velocity of the bulk wave is determined by physical properties (elastic constant and the like) of materials of films. Therefore, the wavelength in each film decreases with increasing the resonant frequency. In other words, in order to obtain a higher resonant frequency, it is necessary to decrease the film thicknesses of the piezoelectric film and electrodes.
Therefore, when a high resonant frequency such as 5 GHz or more is required, the film thickness of the piezoelectric film needs to be set extremely thin. For example, when zinc oxide (ZnO) is used as a material for the piezoelectric film, the film thickness thereof needs to be set at approximately 0.27 μm in order to obtain the resonant frequency of 5 GHz or more. When the film thickness of the piezoelectric film is made thinner, the distance between the upper and lower electrodes naturally becomes short. Electrostatic capacitance between the upper and lower electrodes is increased accordingly.
Meanwhile, when a filter is configured by using a plurality of film bulk acoustic resonators, the filter characteristics greatly depend on a capacitance ratio of electrostatic capacitance of a parallel arm resonator to electrostatic capacitance of a series arm resonator (Cp/Cs) and a capacitance product (Cp·Cs). Here, “Cp” means electrostatic capacitance of a parallel arm resonator and “Cs” means electrostatic capacitance of a series arm resonator. For example, input/output impedance of the filter depends on the capacitance product (Cp·Cs), and to make the capacitance product to be 50 Ω, values of Cp and Cs need to be adjusted to satisfy the following equation:                               Cp          ·          Cs                =                  1                                    (                              2                ⁢                                                                  ⁢                π                ⁢                                                                  ⁢                                                      f                    0                                    ·                  50                                            )                        2                                              (        1        )            where, f0 is the resonant frequency. Referring to the equation (1), it is obvious that the optimum capacitance product (Cp·Cs) decreases with increasing the resonant frequency f0.
However, as described above, in order to make the resonant frequency higher in the film bulk acoustic resonator, the film thickness of the piezoelectric film needs to be set thin. Therefore, in contrast to the above, the electrostatic capacitance per unit area increases with increasing the resonant frequency. Hence, in order to obtain a high resonant frequency while maintaining the input/output impedance at 50 Ω, overlap between the upper and lower electrodes (electrode area) needs to be set small. For example, when zinc oxide (ZnO) is used as a material for the piezoelectric film to set the resonant frequency to be 5 GHz or more, it is required to reduce the electrode area to approximately 5000 μm2 or less.
However, the piezoelectric film used for the film bulk acoustic resonator is not composed of a single crystal piezoelectric material but of c-axis oriented grains of finite sizes, and therefore if the electrode area is set extremely small, an influence of the c-axis oriented grains cannot be ignored. Thus, there has been a problem that the resonance characteristics are degraded. This kind of problem becomes markedly when the electrode area is approximately 5000 μm2 or less. Therefore, it has hitherto been difficult to obtain a resonant frequency of 5 GHz or more while the degradation in the resonance characteristics is reduced.